Spindle solutions, hyperscalars and smooth uplifts

TL;DR

This work constructs and analyzes $AdS_3\times Y_7$ solutions in type IIB supergravity with $Y_7$ as a smooth $S^5$ bundle over a spindle $\Sigma(n_N,n_S)$ using a $D=5$ STU gauged supergravity coupled to a charged hyperscalar. It treats both coprime and non-coprime spindles, including cases where the hyperscalar vanishes at the poles and yields nonzero $p_B$ flux, revealing a rich landscape of solutions and potential RG-flow endpoints from STU AdS$_3$ to hyperscalar AdS$_3$. The central charge is computed both from direct BPS analysis and via equivariant localization, with an off-shell extremization that accounts for discrete flux data in the non-coprime case; the hyperscalar spectrum distinguishes inequivalent uplifts sharing the same spindle data. The results illuminate how hyperscalar deformations trigger IR fixed points and map to dual $d=2$ SCFT data, providing a framework for exploring RG flows and extending to related AdS horizons and M-theory uplifts.

Abstract

We construct $AdS_3\times Y_7$ solutions of type IIB supergravity, where $Y_7$ is a smooth $S^5$ bundle over a spindle $Σ(n_N,n_S)$, which are dual to $\mathcal{N}=(0,2)$ SCFTs in $d=2$. The solutions are constructed using the $D=5$ STU $U(1)^3$ gauged supergravity theory coupled to a hyperscalar charged under $U(1)_B$. We investigate spindle solutions with two new features: first, we allow $(n_N,n_S)$ to be non-coprime integers, including orbifolds of the round $S^2$, which can lead to non-unique, inequivalent uplifts, distinguished by the hyperscalar spectra, for given magnetic flux through the spindle. Second, we also allow the hyperscalar to vanish at the poles leading to solutions carrying non-vanishing $U(1)_B$ flux. The new hyperscalar $AdS_3$ solutions can naturally arise as the endpoint of RG flows, triggered by relevant hyperscalar deformations of the $AdS_3$ solutions of the STU model.

Figures (3)

• Figure 1: Possible RG flows between various solutions. We argue that all of the $AdS_3\times \Sigma$ solutions with non-vanishing hyperscalar can be obtained from an RG flow from an $AdS_3\times \Sigma$ solution of the STU model in the anti-twist class, with the same orbifold data. We have also indicated how the solutions could be related by RG flows across dimensions after compactifying $\mathcal{N}=4$ SYM or LS on a spindle with the same spindle data, with some subtleties noted in the text.
• Figure 2: Summary of results. We have set $\kappa=+1$.
• Figure 3: Metric, scalar functions and gauge fields for the solution with $(n_N, n_S)=(1,16)$ in table \ref{['table3']}.